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A Note on Occupation Times of Stationary Processes

Dublin Core		PKP Metadata Items	Metadata for this Document
1.	Title	Title of document	A Note on Occupation Times of Stationary Processes
2.	Creator	Author's name, affiliation, country	Marina Kozlova; Abo Akademi University, Finland
2.	Creator	Author's name, affiliation, country	Paavo Salminen; Abo Akademi University, Finland
3.	Subject	Discipline(s)
3.	Subject	Keyword(s)
4.	Description	Abstract	Consider a real valued stationary process $X={X_s:, s\in R}$. For a fixed $t\in R$ and a set $D$ in the state space of $X$, let $g_t$ and $d_t$ denote the starting and the ending time, respectively, of an excursion from and to $D$ (straddling $t$). Introduce also the occupation times $I^+_t$ and $I^-_t$ above and below, respectively, the observed level at time $t$ during such an excursion. In this note we show that the pairs $(I^+_t, I^-_t)$ and $(t-g_t, d_t-t)$ are identically distributed. This somewhat curious property is, in fact, seen to be a fairly simple consequence of the known general uniform sojourn law which implies that conditionally on $I^+_t + I^-_t = v$ the variable $I^+_t$ (and also $I^-_t$) is uniformly distributed on $(0,v)$. We also particularize to the stationary diffusion case and show, e.g., that the distribution of $I^-_t+I^+_t$ is a mixture of gamma distributions.
5.	Publisher	Organizing agency, location
6.	Contributor	Sponsor(s)
7.	Date	(YYYY-MM-DD)	2005-06-09
8.	Type	Status & genre	Peer-reviewed Article
8.	Type	Type
9.	Format	File format	PDF
10.	Identifier	Uniform Resource Identifier	http://ecp.ejpecp.org/article/view/1138
10.	Identifier	Digital Object Identifier	10.1214/ECP.v10-1138
11.	Source	Journal/conference title; vol., no. (year)	Electronic Communications in Probability; Vol 10
12.	Language	English=en
14.	Coverage	Geo-spatial location, chronological period, research sample (gender, age, etc.)
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